Uniform Circular Motion
For radius R and constant speed v, angular speed omega = v/R and centripetal acceleration has magnitude v squared over R directed radially inward.
Why this shows up in the exam
Turning vehicles · Clock-hand tip motion · Orbital and rotating-machine estimates
Learn the idea
Constant speed around a circle still has inward acceleration because the velocity direction continually changes. The velocity arrow is tangent to the circle and rotates even when its length is fixed. The acceleration points toward the centre and supplies this directional change.
🧠 Memory hook: Uniform circular means constant speed, changing velocity, inward acceleration.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = omega R — relation between linear and angular speed
- a_c = v²/R = omega² R — centripetal acceleration magnitude
- Delta v = 2v sin(Delta theta/2) — velocity-vector change over angular displacement
How to approach it
- 1Mark tangent velocity and inward radius
- 2Relate period, omega, speed, and radius
- 3Use vector geometry for changes over a finite angle
Common slip-ups that cost marks
- •Calling acceleration zero because speed is constant
- •Pointing velocity toward the centre
- •Using degrees directly in time-angle formulas without conversion
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
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